Masteries

Offense:
23

Defense:
0

Utility:
7

Start off on a line with a ranged teammate if possible, or someone who can nuke when you stun the enemy, of course be careful if one of them picked up an oracles make sure to kill them first. You want to stay in line as much as possible until lvl 7 at least to make enough gold for your belt and your boots, then tele to where a gank might be possible (prob mid) or top if they are having issues there and your lane partner is able to hold on his own.

If the opposite team is very aggressive make sure to help gank mid as much as possible, if they are playing defensive you can try to jungle a bit for some extra gold to be able to buy your sunfire (yay hidden aoe + health) and sheen (great for the proc and extra mana), with that you can harass enemies and kill minions without them knowing (it's hilarious to see them run around wondering what's hitting them!).

One thing i've noticed is that Eve is great for killing towers if people don't see her coming, with her ultimate and the atk speed you will gain from Malady (and Phantom Dancer if you were doing really good and got the gold for it already) you should be able to take them on your own while your team distracts them somewhere else. Of course this is just personal taste, i like being able to push. Also, even if you were actually with your team at first and managed to kill most of the enemies, now is the time to go and push, the lifesteal will help you stay there without going back to heal (hit minions or jungle if you must until you're full health) and try to clear mid as much as possible, if you see an enemy just sitting on the turret, go to a diff lane and push that.

This is def not the standard Eve build, but it should be fun to try out if you like being sneaky and not too squishy (which is the main reason i don't like full AP build).

Also, depending on your team setup, if you see you have other people who can take towers fast enough you can replace:
Nashor's Tooth (+50% Attack Speed +55 Ability Power +10 Mana Regeneration per 5 UNIQUE Passive: Reduces ability cooldowns by 25%)

For

Zhonya's Ring (+120 Ability Power UNIQUE Passive: Increases Ability Power by 25%.
Activate:Places you in stasis for 2 seconds, making you invulnerable and non-targetable)

It will give you more AP so you can take people out faster, remember to always go for their squishy champs.